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WALTHAM, Mass. — With every cutter who slips past an unwitting Boston defender, the personnel changes made by the Celtics during the offseason become more glaring. Dramatic roster turnover from one year to the next is not unique to the Celtics, but three games into the season this team has been hardly the efficient machine it was near the end of last season.

Doc Rivers is not surprised by this. Nine of the 15 players on the roster were not with the team last season, and with Avery Bradley out of commission until at least mid-December, five of the top nine players in the Celtics’ rotation are newcomers. Rivers anticipated the players needing a few weeks to get fully acclimated to each other, although he did not anticipate them looking as shaky as they did in the first two games of the season, as well as the second half of game No. 3.

One urge during this transition period would be to lean more heavily on established players like Rajon Rondo, Kevin Garnett and Paul Pierce. At least in the case of the latter two, Rivers refuses to make such a move.

“If we can’t win without them on the floor, we just won’t do it,” Rivers said Tuesday at the Celtics’ practice facility. “I told our bench that. We’re going to play them the minutes that I’m giving them, and eventually I’m going to play them the minutes they should get. They’ve got to do something or we won’t win. It’s that simple.”

Rivers’ reasoning is that Pierce, 35, and Garnett, 36, may be able to cover the team’s deficiencies for now, but in the long term giving both players more minutes now actually could hurt the Celtics. The longer those veterans are on the floor, the less time players like Jared Sullinger or Jeff Green receive to learn the system, and the more strain is put on Pierce and Garnett’s bodies. What might lead to an extra win or two over the Wizards or Raptors in November could cost the Celtics a chance to face the Heat in May or June.

Garnett has not exactly been breaking down Rivers’ door to beg for more minutes, either. The 17-year veteran has not played more than 30 minutes in a game since he logged 31:43 in the season-opening loss to Miami. He admitted on Tuesday that he has earned a deserved reputation as a slower starter and a strong finisher, and he recognized the trade-off that playing him more extensively now would have over the course of the season.

“We’re not where we want to be, obviously,” Garnett said. “But when you put in a new system, new guys, you have to expect that there’s going to be some kind of bumps in the road. We’re not different.”

It is ridiculously early to start evaluating Garnett’s plus-minus or net ratings, but even without using advanced statistics it is clear already that the Celtics are better when Garnett is on the court. That was the case last year, when Garnett made the Celtics so much better that his inability to play 48 minutes a night — also known as “not being superhuman” — was the single biggest reason the Celtics did not make it to the NBA Finals.

Nobody can say yet whether that will be the case again this season. Chris Wilcox is being slowly weaned back into the rotation, while Sullinger and Brandon Bass have played together for 18 minutes in a sort of double-power forward lineup. (That accounts for almost a third of the minutes Sullinger has received so far.) Rivers has juggled the lineup in an effort to minimize the need to lean on Garnett or Pierce, who did not address the media on Tuesday.

“When you take Kevin out, you’re not going to get Kevin,” Rivers said. “But I don’t think that’s been an issue. Last year, when he was off the floor, it had a dramatic [effect]. I don’t think that’s been the case so far this year at all. I think the guys that have come in have tried to do what they should do. I think the other guys with them have to do more, too.”

The Wizards visit Boston on Wednesday to complete a home-and-home set, and the Celtics most likely would increase their odds of winning that game if they played Garnett or Pierce for 40-plus minutes. The question is whether that would be worth it, and Rivers has issued a resounding, “no.”